3880:(IRR) method. The internal rate of return is estimated over regular time intervals, and then the results are linked geometrically. For example, if the internal rate of return over successive years is 4%, 9%, 5% and 11%, then the LIROR equals 1.04 x 1.09 x 1.05 x 1.11 – 1 = 32.12%. If the regular time periods are not years, then calculate either the un-annualized holding period version of the IRR for each time interval or the IRR for each time interval firstly, then convert each one to a holding period return over the time interval, a nd then link together these holding period returns to obtain the LIROR.
3836:
the timing of each external flow. Since the difference between the modified Dietz method and the internal rate of return method is that the modified Dietz method is based on a simple rate of interest principle whereas the internal rate of return method applies a compounding principle, the two methods produce similar results over short time intervals, if the rates of return are low. Over longer time periods, with significant flows relative to the size of the portfolio, and where the returns are not low, then the differences are more significant.
2939:
dividends, etc.). Unless this feature of the time-weighted return is the desired objective, it arguably makes the time-weighted method less informative than alternative methodologies for investment performance attribution at the level of individual instruments. For performance attribution at individual security level to be meaningful in many cases depends on the return being different from the share price return. If the individual security return matches the share price return, the transaction timing effect is zero.
43:. External flows refer to the net movements of value into or out of a portfolio, stemming from transfers of cash, securities, or other financial instruments. These flows are characterized by the absence of a concurrent, equal, and opposite value transaction, unlike what occurs in purchases or sales. Furthermore, they do not originate from the income generated by the portfolio's investments, such as interest, coupons, or dividends.
177:
independently of the poor timing of the cash flow at the beginning of Year 2. If all the money had been invested at the beginning of Year 1, the return by any measure would most likely have been 50%. $ 1,500 would have grown by 100% to $ 3,000 at the end of Year 1, and then declined by 25% to $ 2,250 at the end of Year 2, resulting in an overall gain of $ 750, i.e. 50% of $ 1,500. The difference is a matter of perspective.
1200:
1804:
64:
the whole 2-year period to be 0% (which is incidentally the result of applying one of the money-weighted methods). If the cash flow of $ 1,000 at the beginning of Year 2 is ignored, then the simple method of calculating the return without compensating for the flow will be 200% ($ 1,000 divided by $ 500). Intuitively, 200% is incorrect.
63:
Suppose an investor transfers $ 500 into a portfolio at the beginning of Year 1, and another $ 1,000 at the beginning of Year 2, and the portfolio has a total value of $ 1,500 at the end of the Year 2. The net gain over the two-year period is zero, so intuitively, we might expect that the return over
46:
To compensate for external flows, the overall time interval under analysis is divided into contiguous sub-periods at each point in time within the overall time period whenever there is an external flow. In general, these sub-periods will be of unequal lengths. The returns over the sub-periods between
3839:
Like the simple Dietz method, the modified Dietz returns of two or more different constituent assets in a portfolio over the same period can be combined to derive the modified Dietz portfolio return, by taking the weighted average. The weight to be applied to the return on each asset in this case is
3502:
applies a simple rate of interest principle, as opposed to the compounding principle underlying the internal rate of return method, and further assumes that flows occur at the midpoint within the time interval (or equivalently that they are distributed evenly throughout the time interval). However,
2930:
are transactions such as purchases and sales of holdings within a portfolio, in which the cash used for purchases, and the cash proceeds of sales, is also contained in the same portfolio, so there is no external flow. A cash dividend on a stock in a portfolio, which is retained in the same portfolio
3999:
are sometimes treated as interchangeable terms, but the return calculated by a method such as the time-weighted method is the holding period return per dollar (or per some other unit of currency), not per year (or other unit of time), unless the holding period happens to be one year. Annualization,
3835:
is another method that, like the simple Dietz method, applies a simple rate of interest principle. Instead of comparing the gain in value (net of flows) with the initial value of the portfolio, it compares the net gain in value with average capital over the time interval. Average capital allows for
389:
External flows during the period being analyzed complicate the performance calculation. If external flows are not taken into account, the performance measurement is distorted: A flow into the portfolio would cause this method to overstate the true performance, while flows out of the portfolio would
3856:
If the second purchase is later than halfway through the overall period, the gain, which is 5 dollars, is still the same, but the average capital is less than the start value plus half the net inflow, making the denominator of the modified Dietz return less than that in the simple Dietz method. In
3869:
Calculating the "true time-weighted return" depends on the availability of portfolio valuations during the investment period. If valuations are not available when each flow occurs, the time-weighted return can only be estimated by linking returns for contiguous sub-periods together geometrically,
3459:
Other methods exist to compensate for external flows when calculating investment returns. Such methods are known as "money-weighted" or "dollar-weighted" methods. The time-weighted return is higher than the result of other methods of calculating the investment return when external flows are badly
2958:
To calculate the time-weighted return of these particular shareholdings, in isolation from the cash used to purchase the shares, treat the purchase of shares as an external inflow. Then the first sub-period growth factor, preceding the second purchase, when there are just the first 10 shares, is:
2934:
The time-weighted method only captures the effect attributable to the size and timing of internal flows in aggregate (i.e., insofar as they result in the overall performance of the portfolio). This is for the same reason, that the time-weighted method neutralizes the effect of flows. It therefore
2918:
Investment managers are judged on investment activity which is under their control. If they have no control over the timing of flows, then compensating for the timing of flows, applying the true time-weighted return method to a portfolio, is a superior measure of the performance of the investment
932:
Suppose that the portfolio is valued immediately after each external flow. The value of the portfolio at the end of each sub-period is adjusted for the external flow which takes place immediately before. External flows into the portfolio are considered positive, and flows out of the portfolio are
67:
If we add further information however, a different picture emerges. If the initial investment gained 100% in value over the first year, but the portfolio then declined by 25% during the second year, we would expect the overall return over the two-year period to be the result of compounding a 100%
3852:
If the second purchase is earlier than halfway through the overall period, the gain, which is 5 dollars, is still the same, but the average capital is greater than the start value plus half the net inflow, making the denominator of the modified Dietz return greater than that in the simple Dietz
3450:
The poor timing of the second purchase has made no difference to the performance of the investment in shares, calculated using the time-weighted method, compared, for instance, with a pure buy-and-hold strategy (i.e., buying all the shares at the beginning and holding them until the end of the
2938:
The time-weighted return of a particular security, from initial purchase to eventual final sale, is the same, regardless of the presence or absence of interim purchases and sales, their timing, size and the prevailing market conditions. It always matches the share price performance (including
3163:
176:
The time-weighted return appears in this example to overstate the return to the investor, because he sees no net gain. However, by reflecting the performance each year compounded together on an equalized basis, the time-weighted return recognizes the performance of the investment activity
2950:
Let us imagine an investor purchases 10 shares at 10 dollars per share. Then the investor adds another 5 shares in the same company bought at the market price of 12 dollars per share (ignoring transaction costs). The entire holding of 15 shares is then sold at 11 dollars per share.
3576:
939:
1531:
68:
gain ($ 500) with a 25% loss ($ 500). The time-weighted return is found by multiplying together the growth factors for each year, i.e. the growth factors before and after the second transfer into the portfolio, then subtracting one, and expressing the result as a percentage:
3119:
2379:
3981:
To measure returns net of fees, allow the value of the portfolio to be reduced by the amount of the fees. To calculate returns gross of fees, compensate for them by treating them as an external flow, and exclude the negative effect of accrued fees from valuations.
2508:
Consider another example to calculate the annualized ordinary rate of return over a five-year period of an investment that returns 10% p.a. for two of the five years and -3% p.a. for the other three. The ordinary time-weighted return over the five-year period is:
3035:
3476:
of all external flows and the terminal value equal to the value of the initial investment. However, solving the equation to find an estimate of the internal rate of return generally requires an iterative numerical method and sometimes returns multiple results.
3506:
The simple Dietz returns of two or more different constituent assets in a portfolio over the same period can be combined to derive the simple Dietz portfolio return, by taking the weighted average. The weights are the start value plus half the net inflow.
2493:
3445:
3860:
No matter how late during the period the second purchase of shares occurs, the average capital is greater than 100, and so the
Modified Dietz return is less than 5 percent. This is still noticeably less than the 10 percent time weighted return.
2292:
3623:
2931:
as the stock, is a flow from the stock to the cash account within the portfolio. It is internal to the portfolio, but external to both the stock and the cash account when they are considered individually, in isolation from one another.
1524:
If the portfolio is valued immediately before each flow instead of immediately after, then each flow should be used to adjust the starting value within each sub-period, instead of the ending value, resulting in a different formula:
3747:
2149:
47:
external flows are linked geometrically (compounded) together, i.e. by multiplying together the growth factors in all the sub-periods. The growth factor in each sub-period is equal to 1 plus the return over the sub-period.
3130:
3848:
Referring again to the scenario described in
Examples 4 and 5, if the second purchase occurs exactly halfway through the overall period, the modified Dietz method has the same result as the simple Dietz method.
1195:{\displaystyle 1+R={\frac {M_{1}-C_{1}}{M_{0}}}\times {\frac {M_{2}-C_{2}}{M_{1}}}\times {\frac {M_{3}-C_{3}}{M_{2}}}\times \cdots \times {\frac {M_{n-1}-C_{n-1}}{M_{n-2}}}\times {\frac {M_{n}-C_{n}}{M_{n-1}}}}
2954:
The second purchase appears to be badly timed, compared with the first. Is this poor timing apparent, from the time-weighted (holding-period) return of the shares, in isolation from the cash in the portfolio?
1799:{\displaystyle 1+R={\frac {M_{1}}{M_{0}+C_{0}}}\times {\frac {M_{2}}{M_{1}+C_{1}}}\times {\frac {M_{3}}{M_{2}+C_{2}}}\times ...\times {\frac {M_{n-1}}{M_{n-2}+C_{n-2}}}\times {\frac {M_{n}}{M_{n-1}+C_{n-1}}}}
167:
3521:
3207:
575:
31:, with each sub-period weighted according to its duration. The time-weighted method differs from other methods of calculating investment return, in the particular way it compensates for external flows.
3046:
2608:
3254:
848:
3971:
2802:
2298:
3376:
2935:
does not capture the performance of parts of a portfolio, such as the performance due to individual security-level decisions, so effectively as it captures the overall portfolio performance.
922:
649:
2965:
248:
2870:
3810:
384:
3301:
2658:
2392:
3870:
using sub-periods at the end of which valuations are available. Such an approximate time-weighted return method is prone to overstate or understate the true time-weighted return.
2187:
173:
We can see from the time-weighted return that the absence of any net gain over the two-year period was due to bad timing of the cash inflow at the beginning of the second year.
3778:
3387:
2715:
2910:
Likewise, the rate of return was -3% for three years, which appears in the power of three on the 0.97 factor. The result is then annualized over the overall five-year period.
2835:
2685:
3484:
investments, because the principal partner (the investment manager) has greater control over the timing of cash flows, rather than the limited partner (the end investor).
2229:
3659:
3582:
2223:
Over a period of a decade, a portfolio grows by a continuous rate of return of 5% p.a. (per annum) over three of those years, and 10% p.a. over the other seven years.
2905:
2033:
2005:
1974:
1943:
1896:
1865:
1499:
1401:
1370:
1339:
1292:
1261:
764:
737:
706:
679:
476:
449:
418:
305:
278:
3325:
3683:
2213:
2060:
1916:
1830:
1519:
1472:
1448:
1421:
1312:
1226:
325:
3876:
is another such method that is sometimes used to approximate the true time-weighted return. It combines the true time-weighted rate of return method with the
3472:. Like the true time-weighted return method, the internal rate of return is also based on a compounding principle. It is the discount rate that will set the
3696:
2093:
3503:
the Simple Dietz method is unsuitable when such assumptions are invalid and will produce different results from those of other methods in such a case.
3158:{\displaystyle {\text{Product of sub-period growth factors}}={\text{first sub-period growth factor}}\times {\text{second sub-period growth factor}}}
3571:{\displaystyle {\text{Simple Dietz return}}={\frac {\text{gain or loss}}{{\text{start value}}+{\frac {1}{2}}\times {\text{net inflow}}}}}
74:
3114:{\displaystyle {\frac {\text{End value}}{\text{start value}}}={\frac {15\times 11}{15\times 12}}={\frac {165}{180}}=0.91666\ldots }
3169:
484:
2515:
3213:
2877:
The length of time over which the rate of return was 10% was two years, which appears in the power of two on the 1.1 factor:
772:
3921:
2374:{\displaystyle ={\text{start value}}\times e^{\left(0.05\times {\frac {3}{10}}+0.10\times {\frac {7}{10}}\right)\times 10}}
3896:, etc.) give identical results - it is only the various ways they handle flows that makes them different from each other.
2728:
3030:{\displaystyle {\frac {\text{End value}}{\text{start value}}}={\frac {10\times 12}{10\times 10}}={\frac {120}{100}}=1.2}
4072:
3338:
3040:
and growth factor over the second sub-period, following the second purchase, when there are 15 shares altogether, is:
859:
586:
4115:
4105:
39:
The time-weighted return is a measure of the historical performance of an investment portfolio which compensates for
191:
2841:
2488:{\displaystyle 5\%\times {\frac {3}{10}}+10\%\times {\frac {7}{10}}={\frac {5\%\times 3+10\%\times 7}{10}}=8.5\%}
3784:
336:
3260:
2614:
2084:. The overall rate of return is the time-weighted average of the continuous rate of return in each sub-period.
4140:
4028:
3440:{\displaystyle ={\frac {{\text{End value}}-{\text{start value}}}{\text{start value}}}={\frac {11-10}{10}}}
2157:
1454:
If there is an external flow occurring at the end of the overall period, then the number of sub-periods
3753:
2691:
2808:
2664:
4130:
2287:{\displaystyle {\text{End value}}={\text{start value}}\times e^{0.05\times 3}\times e^{0.10\times 7}}
4100:
Carl Bacon. Practical
Portfolio Performance Measurement and Attribution. West Sussex: Wiley, 2003.
2386:
The continuous time-weighted rate of return over the ten-year period is the time-weighted average:
4013:
3889:
3877:
3629:
3618:{\displaystyle {\text{Gain or loss}}={\text{end value}}-{\text{start value}}-{\text{net inflow}}}
3469:
1474:
matches the number of flows. However, if there is no flow at the end of the overall period, then
4000:
which means conversion to an annual rate of return, is a separate process. Refer to the article
3918:
method is not a competing method of compensating for flows. It is simply the natural logarithm
4018:
3893:
3832:
3826:
2883:
2010:
1983:
1952:
1921:
1874:
1843:
1477:
1403:
is the net external flow into the portfolio which occurs just before the end of sub-period
1379:
1348:
1317:
1270:
1239:
742:
715:
684:
657:
454:
427:
396:
283:
256:
3307:
8:
4135:
4033:
3499:
3493:
3665:
2007:
is the net external flow into the portfolio which occurs at the beginning of sub-period
3381:
which is the same as the simple return calculated using the change in the share price:
2198:
2045:
1901:
1815:
1504:
1457:
1433:
1406:
1297:
1211:
310:
3853:
method. In this case, the
Modified Dietz return is less than the Simple Dietz return.
4111:
4101:
4068:
3742:{\displaystyle {\text{Simple Dietz return}}={\frac {5}{100+{\frac {1}{2}}\times 60}}}
3473:
2144:{\displaystyle {\text{End value}}={\text{start value}}\times e^{r_{\mathrm {log} }t}}
28:
24:
2922:
3888:
If there are no external flows, then all of these methods (time-weighted return,
2942:
See
Example 4 below, which illustrates this feature of the time-weighted method.
4023:
4001:
3995:
3905:
3515:
Applying the Simple Dietz method to the shares purchased in
Example 4 (above):
3481:
2191:
3857:
this case, the
Modified Dietz return is greater than the Simple Dietz return.
3480:
The internal rate of return is commonly used for measuring the performance of
4124:
55:
To illustrate the problem of external flows, consider the following example.
4110:
Bruce J. Feibel. Investment
Performance Measurement. New York: Wiley, 2003.
927:
4067:, William G. Bain, Woodhead Publishing; 1 edition (March 13, 1996)
2923:
Internal flows and the performance of elements within a portfolio
162:{\displaystyle (1+1.0)(1-0.25)-1=2.0\times 0.75-1=1.5-1=0.5=50\%}
3817:
which is noticeably lower than the 10% time-weighted return.
2071:
3202:{\displaystyle ={\frac {120}{100}}\times {\frac {165}{180}}}
570:{\displaystyle R={\frac {M_{2}-(M_{1}+C_{1})}{M_{1}+C_{1}}}}
3883:
2603:{\displaystyle (1+0.10)(1+0.10)(1-0.03)(1-0.03)(1-0.03)-1}
3454:
2498:
3249:{\displaystyle ={\frac {120\times 165}{100\times 180}}}
843:{\displaystyle R={\frac {(M_{2}-C_{2})-M_{1}}{M_{1}}}}
185:
The return of a portfolio in the absence of flows is:
3966:{\displaystyle ln\left({\frac {M_{2}}{M_{1}}}\right)}
3924:
3787:
3756:
3699:
3668:
3632:
3585:
3524:
3390:
3341:
3310:
3263:
3216:
3172:
3133:
3049:
2968:
2886:
2844:
2811:
2731:
2694:
2667:
2617:
2518:
2395:
2301:
2232:
2201:
2160:
2096:
2048:
2013:
1986:
1955:
1924:
1904:
1877:
1846:
1818:
1534:
1507:
1480:
1460:
1436:
1409:
1382:
1351:
1320:
1300:
1273:
1242:
1214:
942:
862:
775:
745:
718:
687:
660:
589:
487:
457:
430:
399:
339:
313:
286:
259:
194:
77:
2913:
2797:{\displaystyle (1.1^{2}\times 0.97^{3})^{1/(2+3)}-1}
928:
Time-weighted return compensating for external flows
424:
of the period, adjust the portfolio's initial value
3965:
3804:
3772:
3741:
3677:
3653:
3617:
3570:
3439:
3370:
3319:
3295:
3248:
3201:
3157:
3113:
3029:
2899:
2864:
2829:
2796:
2709:
2679:
2652:
2602:
2487:
2373:
2286:
2207:
2181:
2143:
2054:
2027:
1999:
1968:
1937:
1910:
1890:
1859:
1824:
1798:
1513:
1493:
1466:
1442:
1415:
1395:
1364:
1333:
1306:
1286:
1255:
1220:
1194:
916:
842:
758:
731:
712:of the period, adjust the portfolio's final value
700:
673:
643:
569:
470:
443:
412:
378:
319:
299:
272:
242:
161:
4053:Measuring Investment Performance of Pension Funds
3371:{\displaystyle {\text{Growth factor}}-1=0.1=10\%}
4122:
3332:and the time-weighted holding-period return is:
2722:and after annualization, the rate of return is:
1898:is the portfolio value at the end of sub-period
1294:is the portfolio value at the end of sub-period
917:{\displaystyle 1+R={\frac {M_{2}-C_{2}}{M_{1}}}}
644:{\displaystyle 1+R={\frac {M_{2}}{M_{1}+C_{1}}}}
50:
4085:Pension Funds: Measuring Investment Performance
4055:, Bank Administration Institute, December 1968
243:{\displaystyle R={\frac {M_{2}-M_{1}}{M_{1}}}}
681:into the portfolio just before the valuation
390:cause it to understate the true performance.
2865:{\displaystyle =2.00\ldots \%{\text{ p.a.}}}
327:is the portfolio's return over the period.
3805:{\displaystyle =3.86\%{\text{ (2 d. p.)}}}
3463:
379:{\displaystyle 1+R={\frac {M_{2}}{M_{1}}}}
3864:
3296:{\displaystyle ={\frac {19,800}{18,000}}}
2919:manager, at the overall portfolio level.
2653:{\displaystyle =1.1^{2}\times 0.97^{3}-1}
1521:is one greater than the number of flows.
3985:
3820:
3124:so the overall period growth factor is:
2082:continuous (logarithmic) rates of return
853:and the corresponding growth factor is:
580:and the corresponding growth factor is:
3884:Returns methods in the absence of flows
1501:is zero, and the number of sub-periods
180:
16:Method of calculating investment return
4123:
3899:
3874:Linked Internal Rate of Return (LIROR)
3487:
307:is the portfolio's initial value, and
3455:Comparison with other returns methods
2499:Ordinary time-weighted rate of return
27:, where returns over sub-periods are
3136:Product of sub-period growth factors
1918:, immediately before external flow
654:To compensate for an external flow
393:To compensate for an external flow
13:
4094:
4065:Investment Performance Measurement
3840:the average capital of the asset.
3794:
3460:timed - refer to Example 4 above.
3365:
2854:
2704:
2482:
2461:
2446:
2421:
2399:
2182:{\displaystyle r_{\mathrm {log} }}
2173:
2170:
2167:
2130:
2127:
2124:
1314:, immediately after external flow
156:
14:
4152:
3773:{\displaystyle ={\frac {5}{130}}}
2914:Portfolio performance measurement
2710:{\displaystyle =10.4334\ldots \%}
34:
2830:{\displaystyle =1.0200\ldots -1}
2680:{\displaystyle =0.104334\ldots }
2072:Why it is called "time-weighted"
280:is the portfolio's final value,
3152:second sub-period growth factor
1867:is the initial portfolio value,
1263:is the initial portfolio value,
4077:
4058:
4046:
3144:first sub-period growth factor
2783:
2771:
2759:
2732:
2591:
2579:
2576:
2564:
2561:
2549:
2546:
2534:
2531:
2519:
2066:
811:
785:
536:
510:
105:
93:
90:
78:
1:
4039:
4029:Rate of return on a portfolio
2062:is the number of sub-periods.
1976:is the final portfolio value,
1450:is the number of sub-periods.
1372:is the final portfolio value,
51:The problem of external flows
3843:
3510:
3468:One of these methods is the
2945:
2503:
2218:
58:
7:
4007:
3654:{\displaystyle =165-100-60}
23:is a method of calculating
10:
4157:
3903:
3824:
3491:
420:into the portfolio at the
21:time-weighted return (TWR)
2192:continuous rate of return
2087:In the absence of flows,
2080:is best illustrated with
4014:Internal rate of return
3976:
3890:internal rate of return
3878:internal rate of return
3470:internal rate of return
3464:Internal rate of return
2900:{\displaystyle 1.1^{2}}
2215:is the length of time.
3973:of the growth factor.
3967:
3865:Linked returns methods
3806:
3774:
3743:
3679:
3655:
3619:
3572:
3441:
3372:
3321:
3297:
3250:
3203:
3159:
3115:
3031:
2901:
2866:
2831:
2798:
2711:
2681:
2654:
2604:
2489:
2375:
2288:
2209:
2183:
2145:
2056:
2029:
2001:
1970:
1939:
1912:
1892:
1861:
1826:
1800:
1515:
1495:
1468:
1444:
1417:
1397:
1366:
1335:
1308:
1288:
1257:
1222:
1196:
918:
844:
760:
733:
702:
675:
645:
571:
472:
445:
414:
380:
330:The growth factor is:
321:
301:
274:
244:
163:
4019:Modified Dietz method
3986:Annual rate of return
3968:
3904:Further information:
3894:modified Dietz Method
3833:modified Dietz method
3827:Modified Dietz method
3821:Modified Dietz method
3807:
3775:
3744:
3680:
3656:
3620:
3573:
3442:
3373:
3322:
3298:
3251:
3204:
3160:
3116:
3032:
2902:
2867:
2832:
2799:
2712:
2682:
2655:
2605:
2490:
2376:
2289:
2210:
2184:
2146:
2057:
2030:
2028:{\displaystyle {t+1}}
2002:
2000:{\displaystyle C_{t}}
1971:
1969:{\displaystyle M_{n}}
1940:
1938:{\displaystyle C_{t}}
1913:
1893:
1891:{\displaystyle M_{t}}
1862:
1860:{\displaystyle M_{0}}
1827:
1801:
1516:
1496:
1494:{\displaystyle C_{n}}
1469:
1445:
1418:
1398:
1396:{\displaystyle C_{t}}
1367:
1365:{\displaystyle M_{n}}
1336:
1334:{\displaystyle C_{t}}
1309:
1289:
1287:{\displaystyle M_{t}}
1258:
1256:{\displaystyle M_{0}}
1223:
1197:
919:
845:
761:
759:{\displaystyle C_{2}}
734:
732:{\displaystyle M_{2}}
703:
701:{\displaystyle M_{2}}
676:
674:{\displaystyle C_{2}}
646:
572:
473:
471:{\displaystyle C_{1}}
446:
444:{\displaystyle M_{1}}
415:
413:{\displaystyle C_{1}}
381:
322:
302:
300:{\displaystyle M_{1}}
275:
273:{\displaystyle M_{2}}
245:
164:
4141:Mathematical finance
3922:
3785:
3754:
3697:
3666:
3630:
3583:
3522:
3388:
3339:
3320:{\displaystyle =1.1}
3308:
3261:
3214:
3170:
3131:
3047:
2966:
2884:
2842:
2809:
2729:
2692:
2665:
2615:
2516:
2393:
2299:
2230:
2199:
2158:
2094:
2046:
2011:
1984:
1953:
1922:
1902:
1875:
1844:
1834:time-weighted return
1816:
1532:
1505:
1478:
1458:
1434:
1407:
1380:
1349:
1318:
1298:
1271:
1240:
1230:time-weighted return
1212:
940:
860:
773:
743:
716:
685:
658:
587:
485:
455:
428:
397:
337:
311:
284:
257:
192:
181:Adjustment for flows
75:
4087:. Free Press, 1966.
4034:Simple Dietz method
3900:Logarithmic returns
3702:Simple Dietz return
3527:Simple Dietz return
3500:Simple Dietz method
3494:Simple Dietz method
3488:Simple Dietz method
29:compounded together
3963:
3916:logarithmic return
3802:
3770:
3739:
3678:{\displaystyle =5}
3675:
3651:
3615:
3568:
3437:
3368:
3317:
3293:
3246:
3199:
3155:
3111:
3027:
2897:
2862:
2827:
2794:
2707:
2677:
2650:
2600:
2485:
2371:
2284:
2205:
2179:
2141:
2052:
2025:
1997:
1966:
1935:
1908:
1888:
1857:
1822:
1796:
1511:
1491:
1464:
1440:
1413:
1393:
1362:
1331:
1304:
1284:
1253:
1218:
1192:
914:
840:
756:
729:
698:
671:
641:
567:
468:
441:
410:
376:
317:
297:
270:
240:
159:
3957:
3800:
3768:
3737:
3728:
3703:
3613:
3605:
3597:
3589:
3566:
3563:
3555:
3542:
3537:
3528:
3474:net present value
3435:
3414:
3413:
3408:
3400:
3345:
3291:
3244:
3197:
3184:
3153:
3145:
3137:
3100:
3087:
3058:
3057:
3054:
3019:
3006:
2977:
2976:
2973:
2860:
2474:
2435:
2413:
2356:
2337:
2308:
2244:
2236:
2208:{\displaystyle t}
2108:
2100:
2055:{\displaystyle n}
1911:{\displaystyle t}
1836:of the portfolio,
1825:{\displaystyle R}
1794:
1740:
1668:
1626:
1584:
1514:{\displaystyle n}
1467:{\displaystyle n}
1443:{\displaystyle n}
1416:{\displaystyle t}
1307:{\displaystyle t}
1232:of the portfolio,
1221:{\displaystyle R}
1190:
1142:
1076:
1034:
992:
912:
838:
766:. The return is:
639:
565:
478:. The return is:
374:
320:{\displaystyle R}
238:
25:investment return
4148:
4131:Finance theories
4088:
4083:Dietz, Peter O.
4081:
4075:
4062:
4056:
4050:
3972:
3970:
3969:
3964:
3962:
3958:
3956:
3955:
3946:
3945:
3936:
3811:
3809:
3808:
3803:
3801:
3798:
3779:
3777:
3776:
3771:
3769:
3761:
3748:
3746:
3745:
3740:
3738:
3736:
3729:
3721:
3709:
3704:
3701:
3684:
3682:
3681:
3676:
3660:
3658:
3657:
3652:
3624:
3622:
3621:
3616:
3614:
3611:
3606:
3603:
3598:
3595:
3590:
3587:
3577:
3575:
3574:
3569:
3567:
3565:
3564:
3561:
3556:
3548:
3543:
3540:
3535:
3534:
3529:
3526:
3446:
3444:
3443:
3438:
3436:
3431:
3420:
3415:
3411:
3410:
3409:
3406:
3401:
3398:
3395:
3377:
3375:
3374:
3369:
3346:
3343:
3326:
3324:
3323:
3318:
3302:
3300:
3299:
3294:
3292:
3290:
3279:
3268:
3255:
3253:
3252:
3247:
3245:
3243:
3232:
3221:
3208:
3206:
3205:
3200:
3198:
3190:
3185:
3177:
3164:
3162:
3161:
3156:
3154:
3151:
3146:
3143:
3138:
3135:
3120:
3118:
3117:
3112:
3101:
3093:
3088:
3086:
3075:
3064:
3059:
3055:
3052:
3051:
3036:
3034:
3033:
3028:
3020:
3012:
3007:
3005:
2994:
2983:
2978:
2974:
2971:
2970:
2906:
2904:
2903:
2898:
2896:
2895:
2871:
2869:
2868:
2863:
2861:
2858:
2836:
2834:
2833:
2828:
2803:
2801:
2800:
2795:
2787:
2786:
2770:
2757:
2756:
2744:
2743:
2716:
2714:
2713:
2708:
2686:
2684:
2683:
2678:
2659:
2657:
2656:
2651:
2643:
2642:
2630:
2629:
2609:
2607:
2606:
2601:
2494:
2492:
2491:
2486:
2475:
2470:
2441:
2436:
2428:
2414:
2406:
2380:
2378:
2377:
2372:
2370:
2369:
2362:
2358:
2357:
2349:
2338:
2330:
2309:
2306:
2293:
2291:
2290:
2285:
2283:
2282:
2264:
2263:
2245:
2242:
2237:
2234:
2214:
2212:
2211:
2206:
2188:
2186:
2185:
2180:
2178:
2177:
2176:
2150:
2148:
2147:
2142:
2140:
2139:
2135:
2134:
2133:
2109:
2106:
2101:
2098:
2061:
2059:
2058:
2053:
2034:
2032:
2031:
2026:
2024:
2006:
2004:
2003:
1998:
1996:
1995:
1975:
1973:
1972:
1967:
1965:
1964:
1944:
1942:
1941:
1936:
1934:
1933:
1917:
1915:
1914:
1909:
1897:
1895:
1894:
1889:
1887:
1886:
1866:
1864:
1863:
1858:
1856:
1855:
1831:
1829:
1828:
1823:
1805:
1803:
1802:
1797:
1795:
1793:
1792:
1791:
1773:
1772:
1756:
1755:
1746:
1741:
1739:
1738:
1737:
1719:
1718:
1702:
1701:
1686:
1669:
1667:
1666:
1665:
1653:
1652:
1642:
1641:
1632:
1627:
1625:
1624:
1623:
1611:
1610:
1600:
1599:
1590:
1585:
1583:
1582:
1581:
1569:
1568:
1558:
1557:
1548:
1520:
1518:
1517:
1512:
1500:
1498:
1497:
1492:
1490:
1489:
1473:
1471:
1470:
1465:
1449:
1447:
1446:
1441:
1422:
1420:
1419:
1414:
1402:
1400:
1399:
1394:
1392:
1391:
1371:
1369:
1368:
1363:
1361:
1360:
1340:
1338:
1337:
1332:
1330:
1329:
1313:
1311:
1310:
1305:
1293:
1291:
1290:
1285:
1283:
1282:
1262:
1260:
1259:
1254:
1252:
1251:
1227:
1225:
1224:
1219:
1201:
1199:
1198:
1193:
1191:
1189:
1188:
1173:
1172:
1171:
1159:
1158:
1148:
1143:
1141:
1140:
1125:
1124:
1123:
1105:
1104:
1088:
1077:
1075:
1074:
1065:
1064:
1063:
1051:
1050:
1040:
1035:
1033:
1032:
1023:
1022:
1021:
1009:
1008:
998:
993:
991:
990:
981:
980:
979:
967:
966:
956:
923:
921:
920:
915:
913:
911:
910:
901:
900:
899:
887:
886:
876:
849:
847:
846:
841:
839:
837:
836:
827:
826:
825:
810:
809:
797:
796:
783:
765:
763:
762:
757:
755:
754:
738:
736:
735:
730:
728:
727:
707:
705:
704:
699:
697:
696:
680:
678:
677:
672:
670:
669:
650:
648:
647:
642:
640:
638:
637:
636:
624:
623:
613:
612:
603:
576:
574:
573:
568:
566:
564:
563:
562:
550:
549:
539:
535:
534:
522:
521:
506:
505:
495:
477:
475:
474:
469:
467:
466:
450:
448:
447:
442:
440:
439:
419:
417:
416:
411:
409:
408:
385:
383:
382:
377:
375:
373:
372:
363:
362:
353:
326:
324:
323:
318:
306:
304:
303:
298:
296:
295:
279:
277:
276:
271:
269:
268:
249:
247:
246:
241:
239:
237:
236:
227:
226:
225:
213:
212:
202:
168:
166:
165:
160:
4156:
4155:
4151:
4150:
4149:
4147:
4146:
4145:
4121:
4120:
4097:
4095:Further reading
4092:
4091:
4082:
4078:
4063:
4059:
4051:
4047:
4042:
4010:
3988:
3979:
3951:
3947:
3941:
3937:
3935:
3931:
3923:
3920:
3919:
3908:
3902:
3886:
3867:
3846:
3829:
3823:
3799: (2 d. p.)
3797:
3786:
3783:
3782:
3760:
3755:
3752:
3751:
3720:
3713:
3708:
3700:
3698:
3695:
3694:
3667:
3664:
3663:
3631:
3628:
3627:
3610:
3602:
3594:
3586:
3584:
3581:
3580:
3560:
3547:
3539:
3538:
3533:
3525:
3523:
3520:
3519:
3513:
3496:
3490:
3466:
3457:
3421:
3419:
3405:
3397:
3396:
3394:
3389:
3386:
3385:
3342:
3340:
3337:
3336:
3309:
3306:
3305:
3280:
3269:
3267:
3262:
3259:
3258:
3233:
3222:
3220:
3215:
3212:
3211:
3189:
3176:
3171:
3168:
3167:
3150:
3142:
3134:
3132:
3129:
3128:
3092:
3076:
3065:
3063:
3050:
3048:
3045:
3044:
3011:
2995:
2984:
2982:
2969:
2967:
2964:
2963:
2948:
2925:
2916:
2891:
2887:
2885:
2882:
2881:
2857:
2843:
2840:
2839:
2810:
2807:
2806:
2766:
2762:
2758:
2752:
2748:
2739:
2735:
2730:
2727:
2726:
2693:
2690:
2689:
2666:
2663:
2662:
2638:
2634:
2625:
2621:
2616:
2613:
2612:
2517:
2514:
2513:
2506:
2501:
2442:
2440:
2427:
2405:
2394:
2391:
2390:
2348:
2329:
2322:
2318:
2317:
2313:
2305:
2300:
2297:
2296:
2272:
2268:
2253:
2249:
2241:
2233:
2231:
2228:
2227:
2221:
2200:
2197:
2196:
2166:
2165:
2161:
2159:
2156:
2155:
2123:
2122:
2118:
2117:
2113:
2105:
2097:
2095:
2092:
2091:
2074:
2069:
2047:
2044:
2043:
2014:
2012:
2009:
2008:
1991:
1987:
1985:
1982:
1981:
1960:
1956:
1954:
1951:
1950:
1929:
1925:
1923:
1920:
1919:
1903:
1900:
1899:
1882:
1878:
1876:
1873:
1872:
1851:
1847:
1845:
1842:
1841:
1817:
1814:
1813:
1781:
1777:
1762:
1758:
1757:
1751:
1747:
1745:
1727:
1723:
1708:
1704:
1703:
1691:
1687:
1685:
1661:
1657:
1648:
1644:
1643:
1637:
1633:
1631:
1619:
1615:
1606:
1602:
1601:
1595:
1591:
1589:
1577:
1573:
1564:
1560:
1559:
1553:
1549:
1547:
1533:
1530:
1529:
1506:
1503:
1502:
1485:
1481:
1479:
1476:
1475:
1459:
1456:
1455:
1435:
1432:
1431:
1408:
1405:
1404:
1387:
1383:
1381:
1378:
1377:
1356:
1352:
1350:
1347:
1346:
1325:
1321:
1319:
1316:
1315:
1299:
1296:
1295:
1278:
1274:
1272:
1269:
1268:
1247:
1243:
1241:
1238:
1237:
1213:
1210:
1209:
1178:
1174:
1167:
1163:
1154:
1150:
1149:
1147:
1130:
1126:
1113:
1109:
1094:
1090:
1089:
1087:
1070:
1066:
1059:
1055:
1046:
1042:
1041:
1039:
1028:
1024:
1017:
1013:
1004:
1000:
999:
997:
986:
982:
975:
971:
962:
958:
957:
955:
941:
938:
937:
930:
906:
902:
895:
891:
882:
878:
877:
875:
861:
858:
857:
832:
828:
821:
817:
805:
801:
792:
788:
784:
782:
774:
771:
770:
750:
746:
744:
741:
740:
739:by subtracting
723:
719:
717:
714:
713:
692:
688:
686:
683:
682:
665:
661:
659:
656:
655:
632:
628:
619:
615:
614:
608:
604:
602:
588:
585:
584:
558:
554:
545:
541:
540:
530:
526:
517:
513:
501:
497:
496:
494:
486:
483:
482:
462:
458:
456:
453:
452:
435:
431:
429:
426:
425:
404:
400:
398:
395:
394:
368:
364:
358:
354:
352:
338:
335:
334:
312:
309:
308:
291:
287:
285:
282:
281:
264:
260:
258:
255:
254:
232:
228:
221:
217:
208:
204:
203:
201:
193:
190:
189:
183:
76:
73:
72:
61:
53:
37:
17:
12:
11:
5:
4154:
4144:
4143:
4138:
4133:
4119:
4118:
4108:
4096:
4093:
4090:
4089:
4076:
4073:978-1855731950
4057:
4044:
4043:
4041:
4038:
4037:
4036:
4031:
4026:
4024:Rate of return
4021:
4016:
4009:
4006:
4002:rate of return
3996:rate of return
3987:
3984:
3978:
3975:
3961:
3954:
3950:
3944:
3940:
3934:
3930:
3927:
3906:rate of return
3901:
3898:
3885:
3882:
3866:
3863:
3845:
3842:
3825:Main article:
3822:
3819:
3815:
3814:
3813:
3812:
3796:
3793:
3790:
3780:
3767:
3764:
3759:
3735:
3732:
3727:
3724:
3719:
3716:
3712:
3707:
3688:
3687:
3686:
3685:
3674:
3671:
3661:
3650:
3647:
3644:
3641:
3638:
3635:
3609:
3601:
3593:
3578:
3559:
3554:
3551:
3546:
3532:
3512:
3509:
3492:Main article:
3489:
3486:
3482:private equity
3465:
3462:
3456:
3453:
3448:
3447:
3434:
3430:
3427:
3424:
3418:
3404:
3393:
3379:
3378:
3367:
3364:
3361:
3358:
3355:
3352:
3349:
3330:
3329:
3328:
3327:
3316:
3313:
3303:
3289:
3286:
3283:
3278:
3275:
3272:
3266:
3256:
3242:
3239:
3236:
3231:
3228:
3225:
3219:
3209:
3196:
3193:
3188:
3183:
3180:
3175:
3149:
3141:
3122:
3121:
3110:
3107:
3104:
3099:
3096:
3091:
3085:
3082:
3079:
3074:
3071:
3068:
3062:
3038:
3037:
3026:
3023:
3018:
3015:
3010:
3004:
3001:
2998:
2993:
2990:
2987:
2981:
2947:
2944:
2928:Internal flows
2924:
2921:
2915:
2912:
2908:
2907:
2894:
2890:
2875:
2874:
2873:
2872:
2856:
2853:
2850:
2847:
2837:
2826:
2823:
2820:
2817:
2814:
2793:
2790:
2785:
2782:
2779:
2776:
2773:
2769:
2765:
2761:
2755:
2751:
2747:
2742:
2738:
2734:
2720:
2719:
2718:
2717:
2706:
2703:
2700:
2697:
2687:
2676:
2673:
2670:
2660:
2649:
2646:
2641:
2637:
2633:
2628:
2624:
2620:
2599:
2596:
2593:
2590:
2587:
2584:
2581:
2578:
2575:
2572:
2569:
2566:
2563:
2560:
2557:
2554:
2551:
2548:
2545:
2542:
2539:
2536:
2533:
2530:
2527:
2524:
2521:
2505:
2502:
2500:
2497:
2496:
2495:
2484:
2481:
2478:
2473:
2469:
2466:
2463:
2460:
2457:
2454:
2451:
2448:
2445:
2439:
2434:
2431:
2426:
2423:
2420:
2417:
2412:
2409:
2404:
2401:
2398:
2384:
2383:
2382:
2381:
2368:
2365:
2361:
2355:
2352:
2347:
2344:
2341:
2336:
2333:
2328:
2325:
2321:
2316:
2312:
2304:
2281:
2278:
2275:
2271:
2267:
2262:
2259:
2256:
2252:
2248:
2240:
2220:
2217:
2204:
2175:
2172:
2169:
2164:
2152:
2151:
2138:
2132:
2129:
2126:
2121:
2116:
2112:
2104:
2073:
2070:
2068:
2065:
2064:
2063:
2051:
2037:
2036:
2023:
2020:
2017:
1994:
1990:
1978:
1977:
1963:
1959:
1947:
1946:
1932:
1928:
1907:
1885:
1881:
1869:
1868:
1854:
1850:
1838:
1837:
1821:
1807:
1806:
1790:
1787:
1784:
1780:
1776:
1771:
1768:
1765:
1761:
1754:
1750:
1744:
1736:
1733:
1730:
1726:
1722:
1717:
1714:
1711:
1707:
1700:
1697:
1694:
1690:
1684:
1681:
1678:
1675:
1672:
1664:
1660:
1656:
1651:
1647:
1640:
1636:
1630:
1622:
1618:
1614:
1609:
1605:
1598:
1594:
1588:
1580:
1576:
1572:
1567:
1563:
1556:
1552:
1546:
1543:
1540:
1537:
1510:
1488:
1484:
1463:
1452:
1451:
1439:
1425:
1424:
1412:
1390:
1386:
1374:
1373:
1359:
1355:
1343:
1342:
1328:
1324:
1303:
1281:
1277:
1265:
1264:
1250:
1246:
1234:
1233:
1217:
1203:
1202:
1187:
1184:
1181:
1177:
1170:
1166:
1162:
1157:
1153:
1146:
1139:
1136:
1133:
1129:
1122:
1119:
1116:
1112:
1108:
1103:
1100:
1097:
1093:
1086:
1083:
1080:
1073:
1069:
1062:
1058:
1054:
1049:
1045:
1038:
1031:
1027:
1020:
1016:
1012:
1007:
1003:
996:
989:
985:
978:
974:
970:
965:
961:
954:
951:
948:
945:
929:
926:
925:
924:
909:
905:
898:
894:
890:
885:
881:
874:
871:
868:
865:
851:
850:
835:
831:
824:
820:
816:
813:
808:
804:
800:
795:
791:
787:
781:
778:
753:
749:
726:
722:
695:
691:
668:
664:
652:
651:
635:
631:
627:
622:
618:
611:
607:
601:
598:
595:
592:
578:
577:
561:
557:
553:
548:
544:
538:
533:
529:
525:
520:
516:
512:
509:
504:
500:
493:
490:
465:
461:
438:
434:
407:
403:
387:
386:
371:
367:
361:
357:
351:
348:
345:
342:
316:
294:
290:
267:
263:
251:
250:
235:
231:
224:
220:
216:
211:
207:
200:
197:
182:
179:
171:
170:
158:
155:
152:
149:
146:
143:
140:
137:
134:
131:
128:
125:
122:
119:
116:
113:
110:
107:
104:
101:
98:
95:
92:
89:
86:
83:
80:
60:
57:
52:
49:
41:external flows
36:
35:External flows
33:
15:
9:
6:
4:
3:
2:
4153:
4142:
4139:
4137:
4134:
4132:
4129:
4128:
4126:
4117:
4116:0-471-26849-6
4113:
4109:
4107:
4106:0-470-85679-3
4103:
4099:
4098:
4086:
4080:
4074:
4070:
4066:
4061:
4054:
4049:
4045:
4035:
4032:
4030:
4027:
4025:
4022:
4020:
4017:
4015:
4012:
4011:
4005:
4003:
3998:
3997:
3992:
3983:
3974:
3959:
3952:
3948:
3942:
3938:
3932:
3928:
3925:
3917:
3913:
3907:
3897:
3895:
3891:
3881:
3879:
3875:
3871:
3862:
3858:
3854:
3850:
3841:
3837:
3834:
3828:
3818:
3791:
3788:
3781:
3765:
3762:
3757:
3750:
3749:
3733:
3730:
3725:
3722:
3717:
3714:
3710:
3705:
3693:
3692:
3691:
3672:
3669:
3662:
3648:
3645:
3642:
3639:
3636:
3633:
3626:
3625:
3607:
3599:
3591:
3579:
3557:
3552:
3549:
3544:
3530:
3518:
3517:
3516:
3508:
3504:
3501:
3495:
3485:
3483:
3478:
3475:
3471:
3461:
3452:
3432:
3428:
3425:
3422:
3416:
3402:
3391:
3384:
3383:
3382:
3362:
3359:
3356:
3353:
3350:
3347:
3344:Growth factor
3335:
3334:
3333:
3314:
3311:
3304:
3287:
3284:
3281:
3276:
3273:
3270:
3264:
3257:
3240:
3237:
3234:
3229:
3226:
3223:
3217:
3210:
3194:
3191:
3186:
3181:
3178:
3173:
3166:
3165:
3147:
3139:
3127:
3126:
3125:
3108:
3105:
3102:
3097:
3094:
3089:
3083:
3080:
3077:
3072:
3069:
3066:
3060:
3043:
3042:
3041:
3024:
3021:
3016:
3013:
3008:
3002:
2999:
2996:
2991:
2988:
2985:
2979:
2962:
2961:
2960:
2956:
2952:
2943:
2940:
2936:
2932:
2929:
2920:
2911:
2892:
2888:
2880:
2879:
2878:
2851:
2848:
2845:
2838:
2824:
2821:
2818:
2815:
2812:
2805:
2804:
2791:
2788:
2780:
2777:
2774:
2767:
2763:
2753:
2749:
2745:
2740:
2736:
2725:
2724:
2723:
2701:
2698:
2695:
2688:
2674:
2671:
2668:
2661:
2647:
2644:
2639:
2635:
2631:
2626:
2622:
2618:
2611:
2610:
2597:
2594:
2588:
2585:
2582:
2573:
2570:
2567:
2558:
2555:
2552:
2543:
2540:
2537:
2528:
2525:
2522:
2512:
2511:
2510:
2479:
2476:
2471:
2467:
2464:
2458:
2455:
2452:
2449:
2443:
2437:
2432:
2429:
2424:
2418:
2415:
2410:
2407:
2402:
2396:
2389:
2388:
2387:
2366:
2363:
2359:
2353:
2350:
2345:
2342:
2339:
2334:
2331:
2326:
2323:
2319:
2314:
2310:
2302:
2295:
2294:
2279:
2276:
2273:
2269:
2265:
2260:
2257:
2254:
2250:
2246:
2238:
2226:
2225:
2224:
2216:
2202:
2194:
2193:
2162:
2136:
2119:
2114:
2110:
2102:
2090:
2089:
2088:
2085:
2083:
2079:
2078:time-weighted
2049:
2042:
2041:
2040:
2021:
2018:
2015:
1992:
1988:
1980:
1979:
1961:
1957:
1949:
1948:
1930:
1926:
1905:
1883:
1879:
1871:
1870:
1852:
1848:
1840:
1839:
1835:
1819:
1812:
1811:
1810:
1788:
1785:
1782:
1778:
1774:
1769:
1766:
1763:
1759:
1752:
1748:
1742:
1734:
1731:
1728:
1724:
1720:
1715:
1712:
1709:
1705:
1698:
1695:
1692:
1688:
1682:
1679:
1676:
1673:
1670:
1662:
1658:
1654:
1649:
1645:
1638:
1634:
1628:
1620:
1616:
1612:
1607:
1603:
1596:
1592:
1586:
1578:
1574:
1570:
1565:
1561:
1554:
1550:
1544:
1541:
1538:
1535:
1528:
1527:
1526:
1522:
1508:
1486:
1482:
1461:
1437:
1430:
1429:
1428:
1410:
1388:
1384:
1376:
1375:
1357:
1353:
1345:
1344:
1326:
1322:
1301:
1279:
1275:
1267:
1266:
1248:
1244:
1236:
1235:
1231:
1215:
1208:
1207:
1206:
1185:
1182:
1179:
1175:
1168:
1164:
1160:
1155:
1151:
1144:
1137:
1134:
1131:
1127:
1120:
1117:
1114:
1110:
1106:
1101:
1098:
1095:
1091:
1084:
1081:
1078:
1071:
1067:
1060:
1056:
1052:
1047:
1043:
1036:
1029:
1025:
1018:
1014:
1010:
1005:
1001:
994:
987:
983:
976:
972:
968:
963:
959:
952:
949:
946:
943:
936:
935:
934:
907:
903:
896:
892:
888:
883:
879:
872:
869:
866:
863:
856:
855:
854:
833:
829:
822:
818:
814:
806:
802:
798:
793:
789:
779:
776:
769:
768:
767:
751:
747:
724:
720:
711:
693:
689:
666:
662:
633:
629:
625:
620:
616:
609:
605:
599:
596:
593:
590:
583:
582:
581:
559:
555:
551:
546:
542:
531:
527:
523:
518:
514:
507:
502:
498:
491:
488:
481:
480:
479:
463:
459:
436:
432:
423:
405:
401:
391:
369:
365:
359:
355:
349:
346:
343:
340:
333:
332:
331:
328:
314:
292:
288:
265:
261:
233:
229:
222:
218:
214:
209:
205:
198:
195:
188:
187:
186:
178:
174:
153:
150:
147:
144:
141:
138:
135:
132:
129:
126:
123:
120:
117:
114:
111:
108:
102:
99:
96:
87:
84:
81:
71:
70:
69:
65:
56:
48:
44:
42:
32:
30:
26:
22:
4084:
4079:
4064:
4060:
4052:
4048:
3994:
3990:
3989:
3980:
3915:
3911:
3909:
3887:
3873:
3872:
3868:
3859:
3855:
3851:
3847:
3838:
3830:
3816:
3689:
3588:Gain or loss
3536:gain or loss
3514:
3505:
3497:
3479:
3467:
3458:
3449:
3380:
3331:
3123:
3039:
2957:
2953:
2949:
2941:
2937:
2933:
2927:
2926:
2917:
2909:
2876:
2721:
2507:
2385:
2222:
2190:
2153:
2086:
2081:
2077:
2075:
2038:
1833:
1808:
1523:
1453:
1426:
1229:
1204:
931:
852:
709:
653:
579:
421:
392:
388:
329:
252:
184:
175:
172:
66:
62:
54:
45:
40:
38:
20:
18:
3604:start value
3541:start value
3412:start value
3407:start value
3056:start value
2975:start value
2307:start value
2243:start value
2107:start value
2067:Explanation
4136:Investment
4125:Categories
4040:References
3912:continuous
3612:net inflow
3562:net inflow
2859: p.a.
933:negative.
451:by adding
3844:Example 6
3795:%
3731:×
3646:−
3640:−
3608:−
3600:−
3596:end value
3558:×
3511:Example 5
3451:period).
3426:−
3403:−
3399:End value
3366:%
3348:−
3238:×
3227:×
3187:×
3148:×
3109:…
3081:×
3070:×
3053:End value
3000:×
2989:×
2972:End value
2946:Example 4
2855:%
2852:…
2822:−
2819:…
2789:−
2746:×
2705:%
2702:…
2675:…
2645:−
2632:×
2595:−
2586:−
2571:−
2556:−
2504:Example 3
2483:%
2465:×
2462:%
2450:×
2447:%
2425:×
2422:%
2403:×
2400:%
2364:×
2346:×
2327:×
2311:×
2277:×
2266:×
2258:×
2247:×
2235:End value
2219:Example 2
2111:×
2099:End value
2076:The term
1786:−
1767:−
1743:×
1732:−
1713:−
1696:−
1683:×
1671:×
1629:×
1587:×
1183:−
1161:−
1145:×
1135:−
1118:−
1107:−
1099:−
1085:×
1082:⋯
1079:×
1053:−
1037:×
1011:−
995:×
969:−
889:−
815:−
799:−
508:−
422:beginning
215:−
157:%
139:−
127:−
121:×
109:−
100:−
59:Example 1
4008:See also
2672:0.104334
3106:0.91666
2699:10.4334
2189:is the
1832:is the
1228:is the
708:at the
4114:
4104:
4071:
3991:Return
2816:1.0200
2154:where
1809:where
1205:where
253:where
4112:ISBN
4102:ISBN
4069:ISBN
3993:and
3977:Fees
3910:The
3831:The
3792:3.86
3498:The
2849:2.00
2750:0.97
2636:0.97
2589:0.03
2574:0.03
2559:0.03
2544:0.10
2529:0.10
2343:0.10
2324:0.05
2274:0.10
2255:0.05
2195:and
2039:and
1427:and
124:0.75
103:0.25
19:The
3914:or
3766:130
3715:100
3690:so
3643:100
3637:165
3357:0.1
3315:1.1
3288:000
3277:800
3241:180
3235:100
3230:165
3224:120
3195:180
3192:165
3182:100
3179:120
3098:180
3095:165
3025:1.2
3017:100
3014:120
2889:1.1
2737:1.1
2623:1.1
2480:8.5
710:end
148:0.5
136:1.5
118:2.0
88:1.0
4127::
4004:.
3892:,
3734:60
3649:60
3433:10
3429:10
3423:11
3363:10
3282:18
3271:19
3084:12
3078:15
3073:11
3067:15
3003:10
2997:10
2992:12
2986:10
2472:10
2459:10
2433:10
2419:10
2411:10
2367:10
2354:10
2335:10
154:50
3960:)
3953:1
3949:M
3943:2
3939:M
3933:(
3929:n
3926:l
3789:=
3763:5
3758:=
3726:2
3723:1
3718:+
3711:5
3706:=
3673:5
3670:=
3634:=
3592:=
3553:2
3550:1
3545:+
3531:=
3417:=
3392:=
3360:=
3354:=
3351:1
3312:=
3285:,
3274:,
3265:=
3218:=
3174:=
3140:=
3103:=
3090:=
3061:=
3022:=
3009:=
2980:=
2893:2
2846:=
2825:1
2813:=
2792:1
2784:)
2781:3
2778:+
2775:2
2772:(
2768:/
2764:1
2760:)
2754:3
2741:2
2733:(
2696:=
2669:=
2648:1
2640:3
2627:2
2619:=
2598:1
2592:)
2583:1
2580:(
2577:)
2568:1
2565:(
2562:)
2553:1
2550:(
2547:)
2541:+
2538:1
2535:(
2532:)
2526:+
2523:1
2520:(
2477:=
2468:7
2456:+
2453:3
2444:5
2438:=
2430:7
2416:+
2408:3
2397:5
2360:)
2351:7
2340:+
2332:3
2320:(
2315:e
2303:=
2280:7
2270:e
2261:3
2251:e
2239:=
2203:t
2174:g
2171:o
2168:l
2163:r
2137:t
2131:g
2128:o
2125:l
2120:r
2115:e
2103:=
2050:n
2035:,
2022:1
2019:+
2016:t
1993:t
1989:C
1962:n
1958:M
1945:,
1931:t
1927:C
1906:t
1884:t
1880:M
1853:0
1849:M
1820:R
1789:1
1783:n
1779:C
1775:+
1770:1
1764:n
1760:M
1753:n
1749:M
1735:2
1729:n
1725:C
1721:+
1716:2
1710:n
1706:M
1699:1
1693:n
1689:M
1680:.
1677:.
1674:.
1663:2
1659:C
1655:+
1650:2
1646:M
1639:3
1635:M
1621:1
1617:C
1613:+
1608:1
1604:M
1597:2
1593:M
1579:0
1575:C
1571:+
1566:0
1562:M
1555:1
1551:M
1545:=
1542:R
1539:+
1536:1
1509:n
1487:n
1483:C
1462:n
1438:n
1423:,
1411:t
1389:t
1385:C
1358:n
1354:M
1341:,
1327:t
1323:C
1302:t
1280:t
1276:M
1249:0
1245:M
1216:R
1186:1
1180:n
1176:M
1169:n
1165:C
1156:n
1152:M
1138:2
1132:n
1128:M
1121:1
1115:n
1111:C
1102:1
1096:n
1092:M
1072:2
1068:M
1061:3
1057:C
1048:3
1044:M
1030:1
1026:M
1019:2
1015:C
1006:2
1002:M
988:0
984:M
977:1
973:C
964:1
960:M
953:=
950:R
947:+
944:1
908:1
904:M
897:2
893:C
884:2
880:M
873:=
870:R
867:+
864:1
834:1
830:M
823:1
819:M
812:)
807:2
803:C
794:2
790:M
786:(
780:=
777:R
752:2
748:C
725:2
721:M
694:2
690:M
667:2
663:C
634:1
630:C
626:+
621:1
617:M
610:2
606:M
600:=
597:R
594:+
591:1
560:1
556:C
552:+
547:1
543:M
537:)
532:1
528:C
524:+
519:1
515:M
511:(
503:2
499:M
492:=
489:R
464:1
460:C
437:1
433:M
406:1
402:C
370:1
366:M
360:2
356:M
350:=
347:R
344:+
341:1
315:R
293:1
289:M
266:2
262:M
234:1
230:M
223:1
219:M
210:2
206:M
199:=
196:R
169:.
151:=
145:=
142:1
133:=
130:1
115:=
112:1
106:)
97:1
94:(
91:)
85:+
82:1
79:(
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